Question

Question is in pic please solve it​

Answer 1

Given,

• Side of the signal board = a
• Perimeter of the signal board = 3a = 180 cm

∴ a = 60 cm

Semi perimeter of the signal board = $\sf \frac{3a}{2}$

By using Heron’s formula,

Area of the triangular signal board will be :-

$\sf \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \sf= \sqrt{ (\frac{3a}{2}) \: (\frac{3a}{2} - a) \: ( \frac{3a}{2} - a) \: ( \frac{3a}{2} - a)} \\ \\ \sf = \sqrt{ \frac{3a}{2} \times \frac{a}{2} \times \frac{a}{2} \times \frac{a}{2} } \\ \\ \sf = \sqrt{ \frac{ {3a}^{4} }{16} } \\ \\ \sf= \sqrt{ \frac{ {3a}^{2} }{4} } \\ \\ \sf= \sqrt{ \frac{3}{4} } \times 60 \times 60 \\ \\ \sf=\boxed{ \bf900 \sqrt{3} \: {cm}^{2}}$

Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer is 900√3 cm²

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$\huge\sf\blue{Given}$

✭ Side of an equilateral triangle is a

✭ Perimeter is 180 cm

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$\huge\sf\gray{To \:Find}$

◈ The area of the board using Heron's Formula?

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$\huge\sf\purple{Steps}$

Heron's Formula is given by,

$\underline{\boxed{\sf\sqrt{s(s-a)(s-b)(s-c)}}}$

We shall first find the value of s,

➳ $\sf Half \ Perimeter = \dfrac{180}{2}$

➳ $\sf \green{Half \ Perimeter = 90}$

So now that we are given that perimeter is 180 cm

»» $\sf a+a+a=180$

»» $\sf 3a=180$

»» $\sf a=\dfrac{180}{3}$

»» $\sf \red{a=60}$

Now on substituting the values in the formula,

➝ $\sf \sqrt{s(s-a)(s-b)(s-c)}$

➝ $\sf \sqrt{90(90-60)(90-60)(90-60)}$

➝ $\sf \sqrt{90(30)(30)(30)}$

➝ $\sf \sqrt{90(2700)}$

➝ $\sf \sqrt{2430000}$

➝ $\sf \sqrt{243 \times 10^4}$

➝ $\sf \sqrt{3\times 3\times 3\times 3 \times 3 \times 10^4}$

➝ $\sf 3\times 3 \times 100\sqrt{3}$

➝ $\sf \orange{900\sqrt{3} \ cm^2}$

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